An object returned by the amlps function consists in a list
with various components related to the fit of an additive partial linear
model with the Laplace-P-spline approach.
An amlps object has the following elements:
The formula of the additive model.
Sample size.
Total number of smooth terms.
Number of B-spline basis functions used for the fit.
Chosen penalty order.
The dimension of the latent field. This is equal to the sum of the number of B-spline coefficients and the number of regression parameters related to the covariates in the linear part.
Estimated linear regression coefficients. This is a matrix containing the posterior point estimate, standard deviation and lower/upper bounds of the credible interval.
The estimated B-spline coefficients. This is a list
with q vectors of size K-1 representing the estimated B-spline
amplitudes for each smooth term.
Estimated effective degrees of freedom for each latent field variable.
A matrix returning the observed test statistic and p-value for the approximate significance of smooth terms.
The estimated effective degrees of freedom of the smooth terms.
95% HPD interval for the degrees of freedom of the smooth terms.
The estimated degrees of freedom of the additive model.
The estimated standard deviation of the error.
The maximum a posteriori of the (log) posterior penalty vector.
Covariance matrix of the (log) posterior penalty vector evaluated at vmap.
The family of the posterior distribution for v. It is either "skew-normal" or "gaussian".
The parameterization for the posterior distribution of
v. If the posterior of v belongs to the skew-normal family, then
pendist.params is a matrix with as many rows as the number of smooth
terms q. Each row contains the location, scale and shape parameter
of the skew-normal distribution. If the posterior of v belongs to the
Gaussian family, then pendist.params is a vector of length q,
corresponding to vmap.
The covariance matrix of the latent field evaluated at vmap.
The latent field vector evaluated at vmap.
The fitted response values.
The response residuals.
The adjusted r-squared of the model indicating the proportion of the data variance explained by the model fit.
The data frame.
Oswaldo Gressani oswaldo_gressani@hotmail.fr.
amlps, print.amlps,
plot.amlps